Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers

Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization algorithms were originally developed for centralized, in-memory computation on a single machine; and the few that break away from this mold do not easily incorporate practically important constraints, such as nonnegativity. A new constrained tensor factorization framework is proposed in this paper, building upon the Alternating Direction method of Multipliers (ADMoM). It is shown that this simplifies computations, bypassing the need to solve constrained optimization problems in each iteration; and it naturally leads to distributed algorithms suitable for parallel implementation on regular high-performance computing (e.g., mesh) architectures. This opens the door for many emerging big data-enabled applications. The methodology is exemplified using nonnegativity as a baseline constraint, but the proposed framework can more-or-less readily incorporate many other types of constraints. Numerical experiments are very encouraging, indicating that the ADMoM-based nonnegative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.Comment: Submitted to the IEEE Transactions on Signal Processin

Kinetic and thermodynamic analysis of proteinlike heteropolymers: Monte Carlo histogram technique

Using Monte Carlo dynamics and the Monte Carlo Histogram Method, the simple three-dimensional 27 monomer lattice copolymer is examined in depth. The thermodynamic properties of various sequences are examined contrasting the behavior of good and poor folding sequences. The good (fast folding) sequences have sharp well-defined thermodynamic transitions while the slow folding sequences have broad ones. We find two independent transitions: a collapse transition to compact states and a folding transition from compact states to the native state. The collapse transition is second order-like, while folding is first order. The system is also studied as a function of the energy parameters. In particular, as the average energetic drive toward compactness is reduced, the two transitions approach each other. At zero average drive, collapse and folding occur almost simultaneously; i.e., the chain collapses directly into the native state. At a specific value of this energy drive the folding temperature falls below the glass point, indicating that the chain is now trapped in local minimum. By varying one parameter in this simple model, we obtain a diverse array of behaviors which may be useful in understanding the different folding properties of various proteins.Comment: LaTeX, 16 pages, figures in separate uufile. Requires psfig.sty Minor revision, fixed typo in preprint number (no other changes